Anion effects on electronic structure and electrodynamic properties of the Mott insulator $\kappa -{(\mathrm{BEDT}-\mathrm{TTF})}_2{\mathrm{Ag}}_2{\left(\mathrm{CN}\right)}_3$

The Mott insulator $\kappa -{(\mathrm{BEDT}-\mathrm{TTF})}_2{\mathrm{Ag}}_2{\left(\mathrm{CN}\right)}_3$ forms a highly-frustrated triangular lattice of $S=1/2$ dimers with a possible quantum-spin-liquid state. Our experimental and numerical studies reveal the emergence of a slight charge imbalance between crystallographically inequivalent sites, relaxor dielectric response, and hopping dc transport. In a broader perspective we conclude that the universal properties of strongly-correlated charge-transfer salts with spin liquid state are an anion-supported valence band and cyanide-induced quasidegenerate electronic configurations in the relaxed state. The generic low-energy excitations are caused by charged domain walls rather than by fluctuating electric dipoles. They give rise to glassy dynamics characteristic of dimerized Mott insulators, including the sibling compound $\kappa -(\text{BEDT}-\text{TTF}){}_2{\mathrm{Cu}}_2\left(\mathrm{CN}\right){}_3$.

Figure 1

(a) Sketch of the bis(ethylenedithio)tetrathiafulvalene molecule, called BEDT-TTF. (b) View of BEDT-TTF dimers in the $bc$ plane projected along the direction tilted from the $a$ axis by ${42}^{\circ }$; an almost isotropic triangular lattice is denoted by full thick lines; the interdimer transfer integrals are labeled by $t$ and $t^{\prime }$, while the intradimer transfer integral is labeled by $t_d$; the unit cell is denoted as a rectangle. (c) Side view of extended unit cell of $\kappa$-AgCN. Possible hydrogen bonds between the ${\mathrm{CH}}_2$ endgroups of the BEDT-TTF molecules and ${\mathrm{CN}}^{-}$ groups of the anion network are indicated by full (cyan) lines.

Figure 2

(a) Temperature evolution of the intramolecular vibration ${\nu }_{27}$ in $\kappa$-AgCN. The two Fano functions required to fit the spectra indicate two crystallographically distinct sites. No effect on cooling rate (0.1 and 1 K/min) was observed. Temperature dependence of the (b) resonance frequency and (c) damping.

Figure 3

Real part of the dielectric function ${\varepsilon }^{\prime }$ of $\kappa$-AgCN as a function of temperature. The frequency dependent measurements performed with the ac electric field applied $\mathbf{E}\parallel c$ (left panel) and $\mathbf{E}\parallel a^{*}$ (right panel) both demonstrate the relaxor-ferroelectric behavior.

Figure 4

Relaxed structure of the ${\mathrm{Ag}}_2$(CN)${}_3^{-}$ network in the $bc$ plane projected along the $a$ axis as obtained by DFT calculations. In this configuration, the bridging cyanides at the center (${\mathrm{c}}_1$) and at the corner (${\mathrm{c}}_2$) of the unit cell are aligned antiparallel and directed along the [021] direction. In the each layer, two segregated chains can be identified in which cyanides ${\mathrm{b}}_1$ and ${\mathrm{b}}_2$, and ${\mathrm{b}}_3$ and ${\mathrm{b}}_4$ are arranged in the opposite directions, respectively. Silver is colored in red; carbon and nitrogen of CN groups are colored in blue and orange. The unit cell is marked as a rectangle.

Figure 5

Band structure of $\kappa$-AgCN (black) plotted along the high-symmetry directions. If only the molecular self-standing subsystem is calculated, the generic cation bands (dashed blue) are obtained. Shifting them by 424 meV (red) results in an almost complete coincidence with the band structure calculated for the complete system (black), thus revealing the overall cation-derived band character around the Fermi level. Occupation of the corresponding density of states indicates an integer charge transfer for the half-filled band, as expected from the chemical composition.

Figure 6

(a) Dielectric strength $\mathrm{\Delta }\varepsilon$, (b) distribution of relaxation times ($1-\alpha$), (c) mean relaxation time ${\tau }_0$ of $\kappa$-AgCN as a function of inverse temperature. The inset of (a) shows a double logarithmic plot of the frequency dependence of the real ${\varepsilon }^{\prime }$ and imaginary ${\varepsilon }^{\prime \prime }$ parts of the dielectric function for $\mathbf{E}\parallel a^{*}$ at 50 K. The full lines are fits to a generalized Debye function $\varepsilon \left(\omega \right)-{\varepsilon }_{\mathrm{HF}}=\mathrm{\Delta }\varepsilon /\left[1+{\left(\mathrm{i}\omega {\tau }_0\right)}^{1-\alpha }\right]$; ${\varepsilon }_{\mathrm{HF}}$ is the high-frequency dielectric constant. In (c) the full and dashed lines indicate the Arrhenius slowing down of the primary and secondary relaxation process, respectively.

Figure 7

(a) DC resistivity normalized to room temperature value and (b) logarithmic resistivity derivative of $\kappa$-AgCN versus inverse temperature. The inset displays the normalized dc conductivity as a function of $T^{-1/3}$: the behavior evidences the variable-range hopping in two dimensions, whereas above about 140 K, the behavior crosses over into the nearest-neighbor hopping described by a simple activation.